Evaluate fifth root of 3^4* fifth root of 3^6

$\sqrt[5]{3^{4}} \cdot \sqrt[5]{3^{6}}$

Step 1

Combine using the product rule for radicals.

$\sqrt[5]{3^{4} \cdot 3^{6}}$

Step 2

Multiply $3^{4}$ by $3^{6}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[5]{3^{4 + 6}}$

Add $4$ and $6$ .

$\sqrt[5]{3^{10}}$

Step 3

Raise $3$ to the power of $10$ .

$\sqrt[5]{59049}$

Step 4

Rewrite $59049$ as $9^{5}$ .

$\sqrt[5]{9^{5}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

$9$